The Metric (SI) System

1. The Metric (SI) System Unit 1

2. SI = Systeme Internationale • Used in Science • Used throughout the world (except in U.S.A.) for all measurements • Based on “10s”

3. Base Units • Length = Meters (m) • Mass = Grams (g) (Book says kg) • Volume = Liters (L) • Temperature = Kelvins or Celsius (based on absolute zero: -273ºC = 0 K) • 4 ºC = refrigerator • 20-22 ºC = room temperature • 37 ºC = body temperature

4. Metric Prefixes you MUST Memorize!!!!

5. Measurements can be: • Accurate – Close to the “true” value • Precise – Reproducibility in replicate measurements Precise but not accurate Precise AND accurate Neither accurate nor precise

6. Reading the Meniscus Always read volume from the bottom of the meniscus. The meniscus is the curved surface of a liquid in a narrow cylindrical container.

7. Try to avoid parallax errors. Parallaxerrors arise when a meniscus or needle is viewed from an angle rather than from straight-on at eye level. Incorrect: viewing the meniscusfrom an angle Correct: Viewing the meniscusat eye level

8. Identify the smallest unit that your device accurately measures to. Estimate one digit past that smallest unit. If the smallest division is tenths, you estimate to the 100ths. If it is to the ones, estimate to the tenths. Sig. Figs. in Measurement

9. Use the graduations to find all certain digits There are two unlabeled graduations below the meniscus, and each graduation represents 1 mL, so the certain digits of the reading are… • Lab techniques lab 52 mL.

10. Estimate the uncertain digit and take a reading The meniscus is about eight tenths of the way to the next graduation, so the final digit in the reading is _______. 0.8 mL The volume in the graduated cylinder is 52.8 mL.

11. 10 mL Graduate What is the volume of liquid in the graduate? 6 . mL 6

12. 25mL graduated cylinder What is the volume of liquid in the graduate? . mL 1 1 5

13. Reading the Thermometer Determine the readings as shown below on Celsius thermometers: 3 5 0 . C 8 7 5 . C

15. Your Turn: How many meters? 0.72 m 350 m

16. How many mL? 4800 mL

17. How many cm? 7.15 cm How many mm? 71.5 mm

18. Practice • WS #1 -- Sig Figs in Measurement

19. Scientific Notation • In scientific notation, numbers are written as M x 10n. • “M” must be a number between 0 and 10. • There must be one, and only one number to the left of the decimal point. • e.g. 2.35 x 105 meters • 156000 cm = 1.56 x 105 cm • 0.0000245 km = 2.45 x 10-5 km • If you move the decimal point to the left, you add to the exponent. (Remember: LA) • Scientific Notation helps keep track of significant figures!!!

20. Practice • WS #2 Scientific Notation

21. All non-zero digits are significant 9878 mL has 4 sig figs Significant Digits (Figures) • 403 L has 3 sig figs 504.07 L has 5 sig figs • Zeros appearing between non-zero digits are significant

22. Zeros to the right of a non-zero digit and to the right of a decimal are significant 85.00 has 4 sig figs. 9.000000000 has 10 sig figs. Sig. Figs. (Cont.) • 0.095897 m has 5 sig figs 0.0009 Kg has 1 sig fig • Zeros that appear in front of non-zero digits are not significant

23. Sig. Figs. (Cont.) • Zeros at the end of a number but to the left of a decimal may or may not be significant. If such a zero has been measured or is the first estimated digit, it is significant. If the zero has not been measured or estimated but is just a place holder, it is NOT significant. • 2000 m may contain from 1 to 4 sig. figs depending on how many zeros are placeholders. • E.g. 2.0 x 103 m has 2 significant digits.

24. 28.6 g 3340 cm 0.07080 m 9.8000 L 0.0067000 Kg 20 cars 5.44000 g /8.100 mol How many sig figs in: 5.44 m – 2.6103 m 2.8297  2.83 m 2.654 g + 25.32 g 27.974  27.97 g 1.34 mm x .7488 mm 1.003392  1.00 mm 44.064  44.06 g/mol

25. Practice • WS #3 – Significant Figures

26. Any counting numbers have an infinite number of significant digits. 250 cows has an infinite number of significant digits. Sig. Figs, (Cont.) • Conversion factors are never used to determine significant digits.

27. When adding or subtracting decimals, the answer must have the same number of decimal places as there are in the measurement having the fewest decimal places. 50.2 g – 32 g Adding & Subtracting Sig. Figs. 25.652 g + 32.06 g = ? 57.71 g 42.1 L + 2.05 L = ? 44.15  44.2 L 36.6 ºC – 31.8 ºC 4.8 ºC 18.2  18 g

28. When multiplying or dividing decimals, the answer can have no more significant figures than are in the measurement with the fewest number of significant figures. REMEMBER: Conversion factors are not significant! 50.2 g / 32 g Multiplying & Dividing Sig. Figs. 134 g x 749 g = ? 100,366 g  1.00 x 105 g 42.1 L / 2.00 L = ? 21.05  21.1 L 3.60 x 103 m x 8.932 x 105 m 32.1552 x 108 m2 3.22 x 109 m2 1.56875  1.6 g

29. Practice • WS #4 – Sig Figs in Calculations

30. Percent Error Calculation • The accuracy of an individual value or of an average experimental value can be compared quantitatively with the correct or accepted value by calculating percent error. • Percent error is calculated by subtracting the experimental value from the accepted value, dividing the difference by the accepted value, and then multiplying by 100. Percent error is always the absolute value of your answer.

31. Percent Error Formula

32. Percent Error Example: A student measures the mass and volume of a substance and calculates its density as 1.40 g/mL. The actual value of the density is 1.36 g/mL. What is the percent error of this measurement? % Error = 1.36 g/mL - 1.40 g/mL X 100 1.36 g/mL = 2.94% = 3%

33. Practice • WS #5 – Percent Error Calculations • Don’t forget significant figures!!!